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Scientific Notation

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**Scientific Notation At the conclusion of our time together, you should be able to:**

Define scientific notation Convert numbers into scientific notation Convert scientific notation to a standard number

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**What is Scientific Notation?**

Scientific notation is a way of expressing really big numbers or really small numbers. For very large and very small numbers, scientific notation is more concise.

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**Scientific Notation Consists Of Two Parts:**

A number between 1 and 10 A power of 10 N x 10x

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**M x 10n Scientific Notation M is the coefficient 1<M<10**

10 is the base n is the exponent or power of 10

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Other Examples: 5.45E x 10^6

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**Chemical Compound Quiz**

What do sand and water have in common from a chemical point of view? Oxygen

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**Numbers Less Than 1 Will Have A Negative Exponent.**

A millionth of a second is: sec 1 x 10-6 s 1.0E-6 s x 10^-6 s

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**To Change Standard Form To Scientific Notation…**

Place the decimal point so that there is one non-zero digit to the left of the decimal point. Count the number of decimal places the decimal point has “moved” from the original number. This will be the exponent on the 10. If the original number was less than 1, then the exponent is negative. If the original number was greater than 1, then the exponent is positive.

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**Examples Given: 289 800 000 m Use: 2.898 m (moved 8 places)**

Answer: x 108 m Easier Way = M term smaller, so make n term larger to 108 Given: m Use: m (moved 4 places) Answer: x 10-4 m Easier Way = M term larger, so make n term smaller to 10-4

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**To Change Scientific Notation To Standard Form…**

Simply move the decimal point to the right for positive exponent of 10. Move the decimal point to the left for negative exponent of 10. (Use zeros to fill in places.)

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Example Given: x 106 m Answer: m (moved 6 places to the right) Easier Way = 106 to 100 = n smaller, so make M term larger! Given: x 10-4 m Answer: m (moved 4 places to the left) Easier Way = to 100 = n larger, so make M term smaller!

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**Scientific Notation Let’s see if you can:**

Define scientific notation Convert numbers into scientific notation Convert scientific notation to a standard number

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Testing Skill #5

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**that I have given up hope!!!**

I feel much better now... that I have given up hope!!!

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**Learning Check Express these numbers in Scientific Notation:**

cm cm cm 2 cm cm 4.05 x 105 cm 3.872 x 10-3 cm 3 x 109 cm 2 x 100 cm 4.78 x 10-7 cm

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Scientific Notation Calculations

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**Scientific Notation At the conclusion of our time together, you should be able to:**

Multiply and divide numbers that are in scientific notation Add and subtract numbers that are in scientific notation

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**Example #16 (3 x 102 m)(8 x 10-4 m) Answer: multiply M terms 24**

Add n terms -2 24 x 10-2 m2 Adjust to correct scientific notation 2.4 x 10-1 m2 Adjust to correct number of sig figs 2 x 10-1 m2

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**Example #17 (5.000 x 105 m)/(3500 m) Answer: divide M terms 0.001 428**

Subtract n terms 5 x 105 Adjust to correct scientific notation 1.428 x 102 Adjust to correct number of sig figs 1.4 x 102

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**Example #18 (5.0 x 104 m)(8.230 x 106 m) /(1.99 x 1018 m)**

Answer: multiply and divide M terms m Add and subtract n terms -8 x 10-8 m Adjust to correct scientific notation x 10-7 m Adjust to correct number of sig figs 2.1 x 10-7 m

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Example #13 (5.0 x 10-3 m)-(5.0 x 10-8 m) Answer: can only subtract like powers Adjust to larger power (5.0 x 10-3 m)-( x 10-3 m) = x 10-3 m Adjust to correct number of decimal places 5.0 x 10-3 m Adjust to correct scientific notation

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**Example #14 (5.0 x 10-3 m) + 0.774 m Answer: can only add like powers**

Adjust to larger power ( x 100 m) m = m Adjust to correct number of decimal places 0.779 m Adjust to correct scientific notation 7.79 x 10-1 m

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**Example #15 (5.0 x 10-3 m) + (5.0 x 10-4 m) - 0.009 38 m**

Answer: can only add like powers Adjust to larger power ( x 100 m) + ( m) – m m Adjust to correct number of decimal places m Adjust to correct scientific notation -3.9 x 10-3 m

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**Surveillance should precede salientation.**

Familiar Saying Surveillance should precede salientation. Look before you leap!!!

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**Scientific Notation Let’s see if you can:**

Multiply and divide numbers that are in scientific notation Add and subtract numbers that are in scientific notation

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